We discuss the ability of the smoothed particle hydrodynamics (SPH) method combined with a grid-based solver for the Poisson equation to model mass accretion onto protostars in gravitationally unstable protostellar discs. We scrutinize important features of coupling the SPH with grid-based solvers and numerical issues associated with (1) large number of SPH neighbors and (2) relation between gravitational softening and hydrodynamic smoothing length. We report results of our simulations of razor-thin disc prone to fragmentation and demonstrate that the algorithm being simple and homogeneous captures the target physical processes — disc gravitational fragmentation and accretion of gas onto the protostar caused by inward migration of dense clumps. In particular, we obtain two types of accretion bursts: a short-duration one caused by a quick inward migration of the clump, previously reported in the literature, and the prolonged one caused by the clump lingering at radial distances on the order of 15–25 au. The latter is culminated with a sharp accretion surge caused by the clump ultimately falling on the protostar.